Search

We study the threshold corrections for inclusive deep-inelastic scattering (DIS) and their all-order resummation. Using recent results for the QCD form factor, related anomalous dimensions and Mellin moments of DIS structure functions at four loops we derive the complete soft and collinear contributions to the DIS Wilson coefficients at four loops. For a general $SU(n_c)$ gauge group the results are exact in the large-$n_c$ approximation and for QCD with $n_c=3$ we present precise approximations. We extend the threshold resummation exponent $G^N$ in Mellin-$N$ space to the fifth logarithmic (N$^4$LL) order collecting the terms $\alpha_{\rm s}^{\,3} (\alpha_{\rm s} \ln N)^n$ to all orders in the strong coupling constant $\alpha_{\rm s}$. We study the numerical effect of the N$^4$LL corrections using both the fully exponentiated form and the expansion of the coefficient function in towers of logarithms. As a byproduct, we derive a numerical result for the complete pole structure of the QCD form factor in the parameter of dimensional regularization $\varepsilon$ at four loops., Comment: 43 pages, LaTeX, 10 figures ( Journal version )

We study the threshold corrections to the structure functions in deep-inelastic scattering (DIS) at the fifth logarithmic (N$^4$LL) order of the soft-gluon exponentiation in massless perturbative QCD. Using recent results for the splitting functions and the quark form factor, we derive the fourth-order contribution to the coefficient $f^{\rm q}$ of the form factor and from it the N$^4$LL part of the exponentiation coefficient $B^{\rm DIS}$ in the limit of a large number of colours. An approximation scheme is shown that leads to sufficiently accurate N$^4$LL results for full QCD. The N$^4$LL corrections are small and lead to a further stabilization of the perturbative expansion for the soft-gluon exponent., Comment: 6 pages, LaTeX (PoS style), 4 figures, Contribution to the proceedings of `DIS2019', Torino (Italy), April 2019

We discuss a number of FORM features that are essential in the automatic processing of very large numbers of diagrams as used in the Forcer program for 4-loop massless propagator diagrams. Most of these features are new., Comment: 16 pages, LaTeX (PoS style) using axodraw2.sty. To appear in the proceedings of `Loops & Legs 2016', Leipzig (Germany), April 2016

We briefly discuss recent research on the spin-averaged parton densities of the proton, focusing on some aspects relevant to hard processes at the LHC. Specifically, after recalling the basic framework and the need for higher-order calculations, we address the evolution equations governing the scale dependence of the parton distributions and their solution, schemes for initial conditions and the inclusion of heavy quarks, recent progress on fits to data, and future high-precision constraints from LHC measurements., Comment: 12 pages, LaTeX, 12 figures. Plenary talk presented at DIS 2007, Munich, April 2007. To appear in the proceedings

Previous studies of the kinematic coverage for measuring the photon structure function F_2^gamma at a future 500 GeV e^+e^- linear collider are updated using current estimates of luminosities and important detector parameters. The perturbative expansion for the evolution of F_2^gamma is briefly recalled in view of a recent claim that all existing next-to-leading order analyses of the photon structure are incorrect. A simple illustration is given of the different sensitivities of hadronic and photonic structure functions on the strong coupling constant alpha_s., Comment: 6 pages LaTeX including 7 eps-figures, uses espcrc2.sty (included). Talk presented at PHOTON'99, Freiburg (Germany), May 1999. To appear in the proceedings [Nucl. Phys. B (Proc. Suppl.)]

Results are presented of two studies addressing the scaling violations of deep-inelastic structure functions. Factorization-scheme independent fits to all ep and mu p data on F_2 are performed at next-to-leading order (NLO), yielding alpha_s(M_Z) = 0.114 +- 0.002_exp (+0.006-0.004)_th . In order to reduce the theoretical error dominated by the renormalization-scale dependence, the next-higher order (NNLO) needs to be included. For the flavour non-singlet sector, it is shown that available calculations provide sufficient information for this purpose at x > 10^-2., Comment: 3 pages LaTeX including 4 eps-figures, uses npb.sty. Talk presented at DIS'99, DESY-Zeuthen, April 1999. To appear in the proceedings

Recent results presented in the structure functions working group are briefly summarized for the following topics: The theoretical treatment of heavy quarks in structure functions, higher-order corrections for the leading-twist evolution (including small-x resummations), the present status of the proton's parton densities, and the impact of higher twists on determinations of the strong coupling constant. The reader is referred to Part I for accounts of the transition to the photoproduction region, pion and photon structure results, and high-Q^2 phenomena., Comment: 9 pages Latex including 5 figures (9 eps-files), uses sprocl.sty. Talk presented at DIS'98, Brussels, April 1998. To appear in the proceedings

The QCD treatment of the photon structure is recalled. Emphasis is given to the recently derived momentum sum rule, and to the proper choice of the factorization scheme and/or boundary conditions for the evolution equations beyond the leading order. Parametrizations of the photon's parton content are examined and compared. The small-x behaviour of the photon structure is briefly discussed., Comment: 14 pages LaTeX, including 6 eps-figures. Invited talk presented at PHOTON '97, Egmond aan Zee, The Netherlands, May 1997. To appear in the proceedings

The resummation of $O(\alpha_s^{l+1} \ln^{2l} x)$ terms in the evolution kernels of non--singlet combinations of unpolarized and polarized structure functions is investigated. The agreement with complete calculations up to order $\alpha_s^2$ is demonstrated, and the leading small-$x$ contributions to the three--loop non--singlet splitting functions $P^{\pm}$ are derived. The additional contributions due to the resummed terms are studied numerically for the most important non--singlet structure functions. They are found to be about $1\,\%$ or smaller in the kinematical regions accessible at present and in the foreseeable future., Comment: 10 pages, encoded ps file using uufiles

The QCD treatment of the photon structure beyond the leading order is discussed with emphasis on a proper choice of the factorization scheme and/or the boundary conditions. Recent parametrizations of the photon's parton content are examined and compared. The sensitivity of the photon structure function on the QCD scale parameter is reconsidered., Comment: 8 pages, LateX, 8 figures (not included, hardcopies available upon request), LMU-11/94